I can't believe 29 motorcyclists read your post and none of them bothered to answer. That is what forums are for. I bet those same folks gripe about their posts not being answered. I once posted this question on another forum and got several immediate replies. All of them advise me to use good quality motorcycle oil - especially if the bike has a wet clutch, which yours does. I am no expert but my CL350 is my 7th Honda. As I read through the posts I see a lot of questions that I could have asked but they have 0 responses as well.
Mineral based 15W-50 Motul or AGIP seemed to be the best choice that worked for me. Mineral 10W40 is hard to find.
Always keep the oil change periods(1000 miles or 1500 km) seems short but there is no actual oil filter, just the centrifugal.
Otherwise Your cylinder head won't get enough lubrication and will get heavily worn and noisy.
I have read that you need oil that is specialy made for "wet clutch" engines. It's siad that the oil will say O.K for wet clutch motorcycle engines. (No detergents or aditives!) Then what ever weight that fits your use.